Question

Trigonometry

Answer 1

$\huge\boxed{2\sqrt{29}}$

Use the distance formula:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Substitute in the known values.

$d=\sqrt{(6-2)^2+(-7-3)^2}$

Subtract.

$d=\sqrt{4^2+(-10)^2}$

Find the powers.

$d=\sqrt{16+100}$

Add.

$d=\sqrt{116}$

Find two factors of $116$.

$d=\sqrt{4*29}$

Find the two factors of $4$.

$d=\sqrt{2*2*29}$

Move the pair outside the square root.

$d=\boxed{2\sqrt{29}}$